P&K 3950

Sample: project A (linear regression)

Input data

Current Concentration
[mA] [mg/m3]
6.7 53
7.5 50
7.3 59
8.6 86
9.3 63
10.5 71
10.8 107
13.0 123
12.4 147
13.9 143
13.8 164
14.7 181
15.8 166
16.2 201
17.1 192
17.3 220
17.4 220
17.9 233
18.2 215
18.4 226

Characteristics

Function: y'=B*x+C

Coefficients
b
c
15.92
-66.37
Scatters 14.65
Determination coefficient  0.9519
Average value
xm
ym
13.34
146.0
Calculated values
Sxx
Syy
Sxy
301.9
8.038E+04
4806

List of function values

xy'Confidence intervalTolerance interval n'
  y1y2y3y4 
6.700040.29326.65853.928-3.08583.6715.1011
7.763657.22545.17969.27114.58799.8646.5360
8.827274.15763.60384.71232.151116.168.5139
9.890891.09081.881100.3049.596132.5811.185
10.954108.0299.941116.1066.912149.1314.524
12.018124.95117.68132.2384.091165.8217.925
13.082141.89134.98148.79101.13182.6419.912
14.145158.82151.79165.85118.03199.6119.176
15.209175.75168.11183.39134.78216.7216.242
16.272192.68184.06201.31151.39233.9712.742
17.336209.62199.74219.49167.87251.369.7191
18.400226.55215.24237.85184.23268.867.4188

Confidence interval:

Valid for 95.0 percentage statistical certainty with table value t(18)= 2.1017

Tolerance interval:

Valid for 95.0 percentage statistical certainty with table value v(18)= 1.3847 and a share (1-gamma)=95.0 % of the entire collective

Function comparison (significance test)

Coefficients and scatter of the function:

StatementFunctionsABC
1y'=B*x+C 14.65 15.92 -66.37
2y'=A*x²+B*x+C 14.60 0.2924 8.470 -23.43
3y'=B*ln(x)+C 18.83 187.0 -329.2
4y'=A*ln²(x)+B*ln(x)+C 14.24 141.5 -504.0 497.9
5y'=B*exp(x)+C 47.34 1.559E-06 118.2
6y'=A*exp²(x)+B*exp(x)+C 39.23 -3.647E-14 4.575E-06 106.1

The quadratic regression formula cannot be assumed as better than the linear one.

Test value:1.1201
Table value F(17):4.4546
Statistical certainty:95%

Only statement 1 and 2 are compared.

Characteristics / limits

Name Factor Type Y-value Y(Type) delta Y X
G 1 -- 125     12.020
G+V 1 +V 125 132.05 7.0521 12.463
1.2G+V 1.2 +V 150 156.98 6.9889 14.030
2G+T 2 +T 250 295.69 45.69 22.742
5%G 0.05 -- 6.25     4.5615
10%G 0.1 -- 12.5     4.9541


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